A paint company claims their paint will be completely dry within 45 minutes afte

Question

A paint company claims their paint will be completely dry within 45 minutes after application. Recently, customers have complained drying times are longer than the claimed 45 minutes. A consumer advocate group takes a random sample of 25 paint specimens and records their drying times. The average drying time x is 50. Consider dryng time, for all test specimens, to be normally distributed with = 8 Suppose the claimed drying time is true, that is = 45 minutes, what is the probability of observing a sample mean of x = 50 or greater from a sample size of 257(Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question. Given the sample mean x -50 was actually observed, is it reasonably that the average drying time is truly 45 minutes? Choose all that apply. (Select all that apply.) No, it does not seem reasonable that the true average drying time is 45 minutes It is unlikely to observe a sample mean this large or larger given the claim is true O It seems reasonable that the true drying time is 45 minutes. O There is evidence the drying time is longer, on average There is evidence the drying time is shorter, on average.

Explanation / Answer

as probability is very less:

correct option are:

NO it is not reasonable..........

It is unlikely.........

there is evidence that drying time is longer on average

for normal distribution z score =(X-)/ here mean=       = 45.000 std deviation   == 8 sample size       =n= 25 std error=x=/n= 1.6000 probability = P(X>50) = P(Z>3.13)= 1-P(Z<3.13)= 1-0.9991= 0.0009

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